An analysis of the sensitivity and stability of an uncertain SBM DEA model based on belief degree

The efficiency of decision-making units with multiple inputs and outputs can be evaluated using a nonparametric quantitative method called data envelopment analysis (DEA). DEA is a decision-making technique for determining the efficiency of similar units. As a result of its simplicity and applicability, DEA has attracted the attention of scientists and researchers working in various fields, which has contributed to a rich literature in terms of theoretical development and examples. The early models of DEA with crisp inputs and outputs were based on linear programming. As opposed to fuzzy theory and stochastic programming, uncertain belief theory can be applied in the absence of historical data for inputs and outputs. Therefore, this paper firstly studies the slacks-based measure model of DEA in an uncertain environment, where inputs and outputs are uncertain based on belief degrees. The problem is modeled mathematically, and some properties of the model are demonstrated. The slacks-based measure model with belief-degree input and output uncertainties is also examined for stability and sensitivity. The final step of the study involves reporting our experience with the new uncertain slack-based measure model and the stability radius for each decision-making unit.